Girl in my cl and talking back?

I think you handled it correctly, because you questioned her behaviour but still let her go. This girl has a rough life, and I definitely think she needed to see the teacher. If she is usually a good spoken girl and this once got smart-mouthed, there was a problem. You did the right thing, and it is unfair that students cannot leave if it's very important. Blame the policy, not the student or yourself.